Objectives:
To define and demonstrate the six trigonometric functions
To facilitate using the three most frequently used trigonometric functions
Materials Needed:
Pythagorean Theorem Model Overhead
Overhead Projector
Overhead TI81 Graphing Calculator
TI81 Graphing Calculator/Individual
Spaghetti (12 pieces for each individual) four 3, 4 and 5 cm lengths/each
Glue
Centimeter Grid/Individual
Compass and Protractor
Strategy:
1. Discuss the Pythagorean Theorem
2. Demonstrate the Pythagorean Theorem using spaghetti
3. Calculate 6 word problems demonstrating the Pythagorean Theorem
4. Discuss the trigonometric functions
5. Calculate the same 6 word problems demonstrating the trigonometric
functions
6. Discuss how the trigonometric table is formed
7. Graph the sine and cosine functions
8. Demonstrate the plotting of sine, cosine and tangent on the graphing
calculator
9. Discuss how the answers obtained using the Pythagorean Theorem and
the trigonometric functions compare
10. Demonstrate a Real Life Problem by measuring the height of the wall
in the room using the tangent function
Conclusion:
1. The Pythagorean Theorem gives us the third side of a right triangle when
two sides are given. The trigonometric functions give all sides and
angles of a right triangle when one side and one of the acute angles are
given. It was demonstrated to the class how to find the three sides of
a triangle when two sides are given. This was done by using the
Pythagorean Theorem and the trigonometric functions.
2. Trigonometry allows calculation of the measures of angles in a triangle
when the length of certain sides are known. While we studied right
triangles, trigonometry can also be applied to arbitrary triangles.
References:
Algebra 2 (Prentice Hall Mathematics 1990) Contemporary's Number Power 3 (The Real World Math, 1988)